Conventional NN assisted detection or decoding algorithms introduce tuneable multiplicative weights to the FG and then unfold the message-passing algorithm to an NN system for training and optimization [1]}. In terms of the SPDA, trainable weights can be attached to the messages \(p_{i,j}(x_i)\)  in the corresponding FG, so the updating rule in (REF ) is modified as:
\(q_{i,j}(x_i) = \sum _{x_j}I_{i,j}(x_i, x_j)\varsigma _{j,i}p_{j,i}(x_j),\) 
